MIPROWAVE EMISSION FROM PULSED, RELATIVISTIC
e-BEAM DIODES
II.
THE MULTIRESONATOR MAGNETRON
by
A. Palevsky and G. Bekefi
Preprint PFC/JA-78-5
Plasma Research Report
PRR 78/32
July 1978
MICROWAVE EMISSION FROM PULSED, RELATIVISTIC e-BEAM DIODES*
II.
THE MULTIRESONATOR MAGNETRON
by
A. Palevsky and G. Bekefi
Department of Physics and Research Laboratory of Electronics
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139
Abstract
The design and operating characteristics of relativistic, electron
beam magnetrons are described.
The magnetrons are comprised of a pulsed
field-emission cathode (-360kV, ~15kA, -30nsec) and several coupled resonators embedded in the anode block.
The tubes are designed to work at
fixed frequency, in range from 2.3 to 5GHz.
The peak powers generated
are typically 500 to 1000MW.
*This work was supported by the Air Force Office of Scientific Research
(Grant AFOSR77-3143).
- 2 1.
INTRODUCTION
The magnetron has long been known1,2 to be one of the most efficient
and rugged devices for generating microwaves at decimeter and centimeter
wavelength ranges.
Power levels from tens of watts to hundreds of kilo-
watts can be achieved with conversion efficiencies as high as 80 percent.
In recent years3-9 a new class of pulsed magnetron devices came into
existence capable of extending the existing powers by more than two orders
in magnitude.
This has resulted in the generation of unprecedented powers
in the range of hundreds of megawatts to several gigawatts, (albeit at
reduced efficiences of 10-35 percent).
The advance rests on the develop-
ment, within the last decade, of high voltage pulsed power sources10
which are being utilized to energize these novel microwave tubes.
In conventional magnetrons,1,2 voltages of a few hundred volts to
several tens of kilovolts are applied between the anode block and a
heated, thermionic cathode (Fig. 1).
Typical currents drawn from the
cathode by a combination of thermionic emission and secondary emission 1 1
by back-bombardment of the cathode do not exceed a few hundred amperes.
In contrast, the magnetrons discussed in this paper are furnished with
cold, field emission graphite cathodes capable of delivering as much as
100 kA of current.
This is achieved by applying voltages3, 5 of 200-600
kV across millimeter wide vacuum gaps separating the anode from the cathode.
As described elsewhere,12,13 this pulsed power is supplied by the
"NEREUS" high voltage machine capable of delivering to a 4 ohm matched
load 1.3 kJ of e-beam energy at 600 kV maximum for a period of 30 nsec.
We observe that in order to obtain the aforementioned levels of
field emission, the anode-cathode gap d -
(ra-r c) is necessarily small
(several millimeters), the maximum value depending on the cathode material, surface smoothness, and the applied voltage available 1
(for a
- 3 smooth graphite surface V/d>500 kV/cm).
Thus,
in our magnetrons the
quantity d/ra is in the range from 0.15 to 0.25 and the geometry ap-
proaches that of the so-called1 3 ,'planar magnetron".
On the other hand,
conventional low voltage,, low current tubes operate in the regime
d/r a0.5.
This difference can be quite significant in the design of the
magnetron, because, as we shall see later, the configuration of the rf
electric field in the gap is quite sensitive to the value of d.
Table 1 summarizes some of the design characteristics of several
magnetrons constructed by us.
The main geometrical parameters of inter-
est are the cathode radius rc; the inside radius of the anode block ra;
the radius rv of the vane-type resonator used; the angle $ subtended by
the resonators on axis; the number N of resonators, and the length L of
the anode block.
In all cases studied, the cathodes are machined from
solid, dense graphite blocks (POCO Graphite
).
aluminum, oxygen-free copper or tellurium copper.
The anodes are made from
The last named is pre-
ferred by us because it is-more readily machined than copper.
The power from the magnetrons listed in Table 1 is coupled out into
a section of rectangular waveguide via a single capacitive window cut in
one of the resonators.
Thus, the radiation leaves the system in the
TE0 1
mode of a rectangular output guide.
2. DESIGN CRITERIA
(a) Magnetic Field and Voltage Characteristics
As in the smooth-bore magnetron described in a previous publication 1 3
(henceforth called paper I), the multiresonator magnetron comprises a
cylindrical anode of radius ra enclosing a coaxial cylindrical cathode of
a radius rc as is illustrated in Fig. 1.
The electrons emitted by the
cathode are subjected simultaneously to a uniform quasi-steady axial
magnetic field Bz, and an almost radial, quasi-steady electric field
- 4 E r(r) generated by applying voltage V between the two electrodes.
And,
just like in the smooth-bore magnetron, the onset of an azimuthally ro-
tating Brillouin space-charge cloud requires that Bz exceed the critical
magnetic field B* given by the "Hull criterion", 1 3
B*
-
(m c/ed)[y2
-
1]1/2
Tesla
(1)
where
y
and m
de
( + eV*/mc2);
0
-
(ra - r c)/2r a ,
(2)
and e are the rest mass and charge of an electron, respectively;
V-V* is the diode operating voltage.when Bz-B*.
The resonators cut in the anode block (and they can be of many
1
shapes ) are of crucial importance.
In their absence, as in the case of
the smooth-bore magnetron, the electromagnetic modes in the smooth annular gap can be decomposed into rotating waves whose phase velocities are
always greater than the speed of light c (note that the gap or "interaction-space" as it is often called is in fact a cavity resonator and the
dispersion characteristics are in reality those of an infinite set of
discrete modes rather than waves of continuously variable frequency, as
will be seen below).
But, in the presence of periodically spaced cavi-
ties, a certain set of modes excited in the interaction space have phase
velocities less than c.
Thus, when phase synchronism is established be-
tween any one of these modes n and the sheared space charge (see paper
I
) drifting with velocity veEr(r)/Bz, strong wave-particle interaction
sets in, resulting in efficient conversion of beam energy to electromagnetic energy.
This is quite unlike the smooth-bore system wherein such
synchronism cannot be established and where, consequently, the coupling
13
of energy into a given mode is found to be inefficient.
It is now clear that as Bz is gradually increased beyond B* (at,
WMMMMMMWOMMMM
5 -
-
say, constant V) the space charge drift velocity will slow down sufficiently until, the outermost electron layers comprising the sheared spacecharge cannot move in synchronism with the given mode n.
tions will then cease.
The magnetic field Bz -BH
is determined from the
Strong oscilla-
at which this happens
Buneman-Hartree condition.15
Its rela-
tivistically correct statement 16is
eV
BR /Mc
0
2
= (eBBH/2mc 2 n)(r 2 -_1 21
2)
Bi n/2oc
a
C
-
-
-
(r w /cn) 2 ]1/2
(3)
an
where wn is the oscillation frequency of a given azimuthal mode of mode
number n (n-1,2,3 ... ),
and VBH is the diode operating voltage, V=VBH'
corresponding to the magnetic field
Bz=BBH*
We have seen that strong magnetron oscillations can be expected only
when the magnetron operates within the limits prescribed by the Hull and
the Buneman-Hartree criteria, namely when
B*(V*) < Bz < BBH (VBH)
(4)
This has been confirmed experimentally as is illustrated in Fig. 2. The
two solid lines are from Eqs. 1 and 3 and the dashed line represents the
operating range of our 6 resonator magnetron A6 (see Table 1).
The solid
dot gives the magnetic field Bz and voltage V at peak operating power.
Observe that the magnetron oscillates in mode n-6.
When the anode num-
ber n is changed a different straight line tangent to the Hull parabola
is generated.
decreases.
As n increases at fixed w the slope of the straight line
Conversely, as w is increased at fixed n, the slopes of the
Buneman-Hartree lines increase.
It is clear from the foregoing discus-
sion that Eqs. 1 through 4 are very useful tools in magnetron design.
The following subsection is concerned in the calculations of the frequencies wn which must, of course, be consistent with the requirements
of Eq. 4.
- 6 (b) Dispersion Characteristics
The annular interaction space dwra-rc together with the periodically
spaced cavities can be viewed as a coaxial microwave resonator of compli-
cated geometrical cross section.
Or it can be viewed as a coaxial trans-
mission line operating at a frequency equal to the cutoff frequency.
The
modes of interest which this resonator supports belong to the family of
transverse electric modes (TE or H modes), with the rf magnetic field lying entirely along the z axis.
To compute the frequencies of the natural
modes of oscillation we solve Maxwell's equations under two assumptions.
First, we assume that the cathode and anode are infinitely long along the
z axis, thus making the problem entirely two dimensional; and secondly,
we assume that the electron space-charge which normally occupies part of
the interaction space d is absent.
The justification for both assumptions
will be given later in this subsection.
One then solves
Maxwell's field equations in vacuum for the inter-
action space alone, and for the anode-block resonators alone.
Setting
the rf admittance (or the average Poynting flux) of one equal to the rf
admittance of the other over their common interface leads to a transcendental equation for the desired frequencies wn.
In Fig. 3 are shown plots
of these computer generated admittances as a function of frequency, for
our A6 (N-6) six-vane magnetron.
The points of intersection give wn
There is an infinite number of resonances, but only the lowest few n<N
are of interest.
A more revealing way of presenting this data is illus-
trated in Fig. 4 in the form of a Brillouin dispersion diagram.
The sys-
tem is seen to be highly dispersive: as n and thus the phase angle increase, the phase velocity (given by the slope of a straight line drawn
from the origin) decreases.
The mode labelled n-N/2-3 is the so-called
"7-mode" for which most conventional magnetrons are designed.
- 7 For this mode the rf electric fields in adjacent resonators are 180*
out of phase with one another.
Our magnetrons oscillate preferentially
in n=N-6 or the "27r-mode" (also called
the 0
mode) which is character-
ized by the fact that the rf fields of all resonators are precisely in
phase.
Observe that the phase velocities for the n-3 and n-6 modes
happen to be the same.
But this fact appears to be purely coincidental
and occurs for the A6, and B6 magnetrons only (see Table 1).
eracy can be removed by changing rv and
4
This degen-
of Table 1.
The computed frequencies and the phases are checked experimentally
by a series of "cold tests" carried out as follows.
The magnetron anode
is placed on a test bench together with a dummy metal cathode.
A tiny
probing antenna is embedded in the cathode and is allowed to project
slightly within the interaction space.
be rotated about the z axis.
The entire cathode assembly can
A weak microwave signal is injected into
one of the anode-block resonators, and is detected by the probing antenna.
The transmitter frequency is then swept from 2 to 5 GHz and the resonant
frequencies measured.
quencies.
Table 2 compares the measured and calculated fre-
The agreement is seen to be good, showing that our assumption
of an infinitely long anode block is not serious.
However, this is not
too surprising since the physical length L of our anode is 7.2 cm and is
roughly
equal
the free space wavelength X.
For shorter anodes as
those used in conventional magnetrons 1 where L/X*0.25, the differences118
become significant.
In general, the shorter the length L of the anode
block the shorter is the wavelength Xn compared with that
L-)-.
computed for
We have comfirmed this fact by comparing the frequencies of the A6
and B6 magnetrons which differ from one another in length only.
The phases of adjacent resonators are tested by rotating the cathode
and its probing antenna, and determining the phase of the received signal
- 8 interferometrically for the mode n in question.
It is important to note that in our magnetrons the various modes
are well separated in frequency.
As the number of resonators increases,
the frequency separation decreases; multimoding, unstable operation, and
overall deterioration in performance sets in.
For more than eight reso-
nators, one must generally resort to magnetron strapping,19 rising sun
21
resonator configuration, 2 0 or to coaxial resonator configuration.
Each of these alternatives bringswith it its own difficulties, including
such problems as arcing or rf breakdown at the field levels in question.
Therefore, in these early stages of design, when detailed performances
and questions of materials are still lacking, we purposely avoided the
more complex anode block configurations.
Undoubtedly much will be
learned from the next generation devices which incorporate these ideas.2 2
In addition to the principal resonances discussed above, cold tests
disclose a series of unwanted resonances W' associated with the finite
n
length L of the resonator system. The frequencies of these "axial modes"
depend sensitively on boundary conditions at the ends of the anode block
such as whether the ends are electrically open or closed (or in-between).
All our magnetrons are provided with removable metal end-caps and by re-
moving one end-cap, or both, allows us to test magnetron performance as
a function of axial boundary conditions.
The frequencies of the axial
modes are approximately given by2 3 W 2 . W
+ (nnc/2L)2
,
n = 0,1,2,3
...
.
(5)
We have measured the axial variation of the electric field amplitude of
several axial modes by moving the probing antenna embedded in the cathode
axially, along its length.
Only when the anode has end-caps do the modes
show well-defined nodes in the electric field.
With open ends the anti-
- 9 nodes do not always coincide with the end of the anode and their position
depends on the proximity of other metal surfaces.
be replaced by an effective length Leff*
Then L of Eq. (5) must
We find, typically, that Leff
=1.2L.
In the presence of axial modes, multimoding in the magnetron cannot
be ruled out.
To minimize its occurrence it is necessary that no two
modes lie on the same or on a nearby Buneman-Hartree curve (said differently, the phase velocities of the neighboring modes must be wellseparated).
As is seen from Eq. (3), this requires that the quantities
W'/n and w /n of all modes be as far removed as possible from the quann
n
tity w /n of the mode for which the magnetron is designed.
(The fact
that this criterion is not met in the A6 magnetron for the modes n-3 and
n-6 will be discussed in the next subsection.)
We have seen that the calculated frequencies wn are in satisfactory
agreement with cold tests.
Are the calculations still meaningful under
operating conditions, when a portion of the interaction space is filled
with the dense electron space-charge cloud and when it may well contain
some cathode and anode plasma12 as well?
Here the answer is less cer-
tain; but we believe from our frequency measurement of the n-6 mode and
from some measurements on the n-3 mode, both made under operating conditions, that the mode frequencies are not significantly changed by the
presence of the space-charge cloud (see Table 2).
(c) RF Electric Field Configuration
One of the most characteristic properties of a fully oscillating magnetron is the formation of rotating space-charge "spokes" 2 4 ,2 5 ,2 6 from
the initially smooth unperturbed flow.
The spokes extend from cathode to
anode and they rotate with a speed close to the phase speed of the mode
in question.
Spoke formation is a direct consequence of the adiabaticity
- 10 of the electron motion.
The frequency w n/n in the rotating wave frame
is small compared with the cyclotron frequency, and the principal,
motion of the electrons is therefore an EXB ++B2 drift in the combined dc
z z
and rf electric fields.
In other words, the electrons move predominantly
along instantaneous equipotential lines; they also execute small, second-
order gyro-oscillations about them.
Whether or not a given mode is condusive to strong spoke formation
(and thus to efficient magnetron oscillations) depends on the configuration of its rf electric field.
The purpose of this subsection is to
examine the fields of the 'N mode" (n-3) and the "27r mode" (n=6) of our
six cavity magnetron and then draw qualitative conclusions from the respective comparisons.
To this end we will assume (to the lowest degree
of approximation) that the rf fields are unchanged by the presence of
the space charge.
This may not be too harsh .an assumption at least in
the vacuum region between the anode r-ra and the original surface of the
Brillouin cloud r-r
(see paper I) before spoke formation took place.
A solution of Maxwell's equations in the empty interaction space
d-r a-rc is readily performed17 and the computer generated results are il.lustrated in Fig. 5. The diagrams represent the electric field lines for
modes n-3 and n-6.
Good spoke formation requires an "equal mix" of radial
and azimuthal field components.
It is seen that the n-6 mode is likely to
be somewhat better in forming spokes than the n-3 mode.
This may well be
the reason why in our experiments much more power is achieved in the
former than in the latter.
Interestingly, exactly the reverse situation
occurs in conventional magnetrons.
the familiar
Figure 6 shows our computations for
ten vane high power HP10V tube.
This tube is normally
strapped but in our computations we neglect strapping since it is not
really relevant to the present discussion.
We see in Fig. 6 that now the
- 11 7r-mode (n=N/2-5) is probably very efficient in forming spokes but the
2w-mode (n-10) does poorly.
In addition, the rather strong azimuthal
field, associated with the 2w-mode, midway between the resonators tends
to cause a dephasing every half period.
The reason is obvious from the
electric field plots which show that the n-10 mode has strong azimuthal
field component but rather weak radial electric fields.
The n-5 mode,
on the other hand, has well-developed field components along both directions.
These facts tend to substantiate the lack of success27 of oper-
ating conventional magnetrons in the "2w-mode". However, 2w-mode opera-
tion may well be an advantage since, as is seen from Figs. 3 and 4, this
mode is well-separated from the others.
The differences in the field configurations of a given mode n in
the relativistic magnetron and a conventional magnetron come from differences in the gap widths d.
Our relativistic magnetrons have smaller
gaps than typical conventional magnetrons.
For example, we see from
Figs. 5 and 6 that our tube A6 has a gap approximately one-half that of
HP10V tube.
As a result of the proximity of the metal electrodes, the
azimuthal electric fields in the A6 tube tend to be "shorted out", thus
weakening the azimuthal compared with the radial electric field components.
To obtain comparable gap widths in the two types of tubes, and thus cause
them to operate under similar conditions, the relativistic magnetron needs
to be operated at higher potentials than are available to us, typically at
600-1200kV.
place
At these potentials sufficient field emission will take
with gaps 1 to 2cm in width.
The magnitudes of the rf electric and rf magnetic fields permissible
in a practical device are governed by several considerations.
The rf
electric field is limited by breakdown even for good vacua (pressure
104 Torr).
One cause of breakdown comes about through the evolution of
- 12 impurity gases from metal surfaces, leading to the formation of cathode
and anode plasmas.12
Another comes from secondary electron emission at
the surfaces leading to multipacting.28
Fortunately, the occurrence of
breakdown within the magnetron is lessened by the presence of the strong
axial dc magnetic field. 2 9
Limits on the maximum rf electric field apply both to conventional
and relativistic microwave generators.
However, there appears to be also
a limit on the maximum permissible rf magnetic field Bz(rf), which is
peculiar to ultra-high power relativistic devices only.
If the rf magnet-
ic field is too large, then, during one part of the rf cycle, the total
magnetic field (dc plus rf) may become less than the critical magnetic
field B* of Eq. (1).
When this happens, the diode is no longer cutoff
and electrons at the surface of the Brillouin space charge cloud traveling near the speed of light, are collected on the anode in less than half
a period.
To place a limit on the peak rf magnetic field we may assume
that the magnetron operates at or-near the d.c. field given by the
Buneman-Hartree criterion (see Fig. 2).
Bz(rf)
Then,
BBH - B*
(5)
where B* is given by Eq. (1) and BBH by Eq. (3).
If the magnetron oper-
ates at a lower magnetic field, as it often does (see section 3) we can
write more accurately that Bz (rf)SBz max)-B* where now Bz (max) is the
magnetic field for maximum power output.
Thus, for example, we find for
the D6 magnetron (Fig. 12) that Bz (max)-B*=0.4kG. Therefore, the peak
rf magnetic field is 0.4kG, and the corresponding rf electric field is
-120kV/cm.
On the other hand, for the A6 magnetron (Figs. 2 and 11)
Bz (max)-B*-Bz(rf)=2.5kG and the corresponding rf electric field is -750
kV/cm.
It is noteworthy that the D6 magnetron gives consistently lower
power outputs than the A6 magnetron.
- 13 Irrespective of what mechanism is operative in limiting the rf electric field, it places an upper limit on the microwave power P
livered by the device.
Pm
Here P
de-
By energy conservation,
-
oE2(rf)dv
(6)
is the peak power, E(rf) is the amplitude of the electric field,
v is the volume of the magnetron, and Q is the quality factor under operating conditions (that is, it is the "loaded Q" in the presence of the
oscillating space charge).
tric fields are undesirable.
It is clear that high Q's and thus high elecIn our magnetrons the Q's are typically in
the range of 20-40.
We have raised a number of questions which in the absence of a full
theoretical model can be answered only partially.
Such a model does not
exist either for the conventional or the relativistic magnetron.
The
reason is that magnetron oscillations are founded on a nonlinear instability.
Better understanding will have to await detailed analysis pres-
ently underway.
A two-dimensional (r, 6), fully relativistic, electro-
magnetic "particle in cell" computer program is being developed30in
which Maxwell's equations are solved self-consistently in the presence of
space charge.
With its aid we plan to optimize magnetron design and
study the relevant scaling laws with voltage, current, magnetic field,
and frequency as parameters.
3. EXPERIMENTAL RESULTS
Details of the experimental setup, and techniques of measuring volt-
age, current, and magnetic field, etc., are identical to those described
in Refs. 12 and 13.
We shall, therefore, not elaborate on these topics
and proceed directly to a discussion of the experimental results.
- 14 (a)
Current-Voltage Characteristics
Our magnetrons are run at roughly constant diode voltage V lying in
the range VBH<V<V* where V* and VBH are defined in Eqs. (1) and (3) respectively.
B z.
The principal variable is the axial applied magnetic field
Figure 7 shows the voltage and current characteristics for the A6
magnetron measured as a function of B z.
The voltage rises slightly and
the current falls fairly monotomically, results which are typical of all
magnetrons tested by us.
It is noteworthy that, as the magnetic field
passes through its critical value B-B*(B*=4.9kG for the A6 magnetron),
nothing unusual takes place in the current.
This is in complete variance
with similar observations made on the smooth-bore magnetron.13
In the
latter, the current drops precipitously near the Hull cutoff Bz=B*, in
accord with theoretical expectations.
One wonders whether the lack of a noticeable cutoff in a fully oscillating magnetron is due to the strong interactions of the rf fields with
the electrons, causing a sizeable fraction of these to be thrown into
orbitswith large parallel velocities.
These electrons would then move
along magnetic field lines and be eventually collected on the anode (the
current plotted in Fig. 7 is the total, radial plus axial, current).
Slight misalignment or asymmetry could be another, more mundane reason
for large axial currents.
To test this we mount a current-viewing probe
so positioned as to collect virtually all axial current.
trates the results for the D6 magnetron.
Figure 8 illus-
We see that the axial current
is relatively small, and even when we subtract it from the total current,
no pronounced cutoff occurs at B z=B*.
We thus conclude that in a cavity-
loaded magnetron the wave-particle interactions are so violent that the
Hull cutoff (which is a statement13 of energy and momentum conservation
in steady fields only) is largely eliminated from the current character-
- 15 istics of the device.
However, the cutoff remains very much in view
when one examines the rf emission characteristics, as will be shown in
the next subsection.
(b)
Measurements of Microwave Power
The magnetrons under test are mounted in an experimental arrangement very similar to that used in our studies of the smooth-bore magnetron.12,13
The main difference lies in the way the rf power is being
coupled out of the device.
Our principal technique (but also see later)
is to extract power from a single resonator, coupled via a-capacitive
iris to a section of tapered S-band waveguide, as is illustrated in Fig.
9a.
Irises of various widths can be inserted for maximum power output.
The far end of the tapered waveguide is then connected to a power measuring device.
Three devices are used and the results checked against one
another; the observations are found to be mutually consistent.
The one device is a modified form of calorimeter described in Ref.
31.
Here, a section of evacuated waveguide is terminated in a matched
resistive load, and electrically shielded thermistors measure its rise in
temperature.
The second device is a high power, side-wall coupled 50 db
directional coupler.
Most of the energy is absorbed in the matched load.
A calibrated crystal detector whose output is monitored on a fast oscilloscope measures the power in the side-arm after further attenuation is
provided by a precision calibrated attenuator.
The entire system is
either evacuated or filled with SF6 to prevent the occurence of rf breakdown.
In the third detection technique the power emanating from the
waveguide passes through an evacuated, stainless-steel horn having a rectangular aperture 23cmxl7cm.
The radiation from the horn is picked up
by a receiving antenna (a section of open waveguide) placed 3.5m from the
horn.
The signal is then further attenuated and detected with a calibrated
- 16 crystal detector (see also section 2 of paper I, Ref. 13).
The setup is
calibrated in situ to take account of antenna gains and standing waves
caused by room reflections.
The voltage pulse applied across the cathode-anode gap d is roughly
trapezoidal in shape with rise and fall times of -llnsec, and a flattopped portion of ~26nsec duration.
The full width at the half-power
points (FWHM) is -38naec. Figure 10a shows the voltage pulse and Fig.
10b the corresponding current pulse.
The microwave pulse shown in Fig.
10c is substantially narrower having typical FWWH{'s of -17nsec.
One
possible reason for the narrow microwave pulse width is rf breakdown in
the magnetron, or in the associated microwave plumbing.
possibility on the following grounds:
We discard this
we vary the magnetron output power
over more than one order in magnitude with no observable change in pulse
width.
Rather, we ascribe the narrowness to sharp voltage tuning exhib-
ited by the device.
At fixed magnetic field Bz, there is but a narrow
range of AV's over which the magnetron will oscillate.
This explanation
is confirmed by the fact that occasionally (and in particular when Bz is
not optimum), two microwave spikes are observed, one occurring during the
voltage rise and the other during the voltage fall, with a minimum in rf
power during the plateau region in V(t).
In another experiment we gen-
erate a slowly rising 300nsec voltage pulse in the form of a ramp.
Microwave emission occurs only during a very short time interval of 30-40
nsec duration in which the voltage is just "right".
Figure 11 shows a plot of rf power as a function of magnetic field
for the A6 magnetron.
-0.90GW.
Peak power at the magnetic field of ~7.6kG equals
For this device B*-4.9kG and BBH-8 .8kG.
We see that no signif-
icant oscillations zccur at a magnetic field below cutoff B z=B*, and that
the maximum in emission is near (but below) Bz=BBH, in conformity with
- 17 theoretical predictions.
We point out that for all our magnetrons other
than A6, maximum emission occurs at somewhat lower magnetic fields with
Bz (max) closer to B* than to BBH.
Unfortunately it is at present not
possible to determine from analytical considerations either the exact
value of B z(max) for maximum rf power, or the expected anode current I.
Needless to say, both quantities are crucial in magnetron design.
In conventional magnetrons, the cylindrical anode block is customarily open at both ends.
In our magnetrons we make provisions for re-
movable metal end caps.
This allows us to examine the operating charac-
teristics of the device in the presence of one, two, or no end-caps.
We
find in the A6 magnetron that maximum power is achieved when both endcaps are firmly in place.
Tests made on the D6 magnetron again show
that more power is achieved when both end-caps are in place than when
the anode block is open at both ends (no measurements were made in this
magnetron with only one end-cap).
12.
The results are illustrated in Fig.
For a given magnetron system it is not possible to determine, a
priori, the optimum end-cap configuration.
It undoubtedly depends on a
number of parameters, including the method of coupling out the rf power.8,9
It is therefore advantageous to keep the options open.
Two other parameters have been varied optimizing rf power output.
The first is the cathode-anode gap width.
gaps of 5 to 6mm width.
Maximum power is achieved with
For gaps smaller than ~4mm alignment is very
difficult and arcing often occurs.
For gaps larger than -7mm the anode
current and thus the rf power drop significantly.
Note that for a given
magnetron design the gap cannot be varied at will because both B* and w
are quite sensitive functions of d (see section 2).
Secondly, we have varied the axial position of the cathode relative
to the center of the anode block.
In general rf power output can be in-
creased by sliding the cathode axially until its free end coincides ap-
-
18
-
proximately with the center of the anode block.
of the current is emitted from the free
The reason is that most
lcm long section of our 4.0cm
long graphite cathode, as is confirmed by observing anode and cathode
damage patterns (see Refs. 12).
As a result, it is reasonable to expect
maximum wave-particle interaction when the position of maximum electron
emission coincides with the center of the anode-embedded resonators.
(c) Frequency Characteristics
The frequency spectrum of the emitted power is measured by means of
solid state, yttrium garnett dispersive lines (Chu Associates, Harvard,
Mass.) having frequency ranges from 2.0GHz to 3.lGHz and 2.8 to 4.8GHz.
The received power is divided equally by means of a broad-band hybrid
tee; half the signal is rectified with a calibrated crystal detector and
displayed on a fast oscilloscope.
The other half passes through the dis-
persive line, solid state amplifier (Avantek) and a tunnel diode detector
(Aerteck).
The signal from the detector is likewise displayed on the
aforementioned oscilloscope.
The time delay between the dispersed and
undispersed (reference) signals is nearly lineraly proportional to the
frequency of the radiation.
Typical results are shown in Fig. 13a.
The
clean, single-spiked dispersed signal signifies that the magnetron oscillates predominantly at a single frequency.
We cannot determine the pre-
cise line width of the resonant mode using this technique.
However, we
place an upper limit of 40MHz on its width.
The results of Fig. 13a are for the case when the magnetic field
Bz=B z (max) is adjusted for maximum power output.
havior persists even when Bz
Clean, single mode be-
z max); however, for low magnetic fields
B*sB SB (max), the dispersed signal becomes spiky, suggesting that modez z
breakup is taking place.
This is illustrated in Fig. 13b.
multimoding can occur as is shown in Fig. 13c.
Alternately,
At very low magnetic
- 19 fields Bz=B* the magnetron oscillations tend to jump into an entirely
different frequency regime as will be discussed momentarily.
The frequency of oscillation of Fig. 13a corresponds to the "2rmode" (n=N-6) as was mentioned already in section 2.
f=4.6GHz.
The frequency
Maximum power output is achieved in this mode.
As the magnet-
ic field is reduced from Bz (max) and B* is approached, the oscillation
frequency drops suddently to a new value of f=2.3GHz.
We believe that
we are now witnessing oscillations in the "Ir-mode" (n-N/2=3).
The fre-
quency spectrum is quite clean but the emitted power is at best an order
of magnitude lower than it is for the n-6 mode.
In section 2 we give tentative reasons for 27t versus n-mode operation.
Another possible reason for "quenching" of the n-mode is the asym-
metric manner in which power is extracted from the magnetron (Fig. 9a).
Since only one resonator is loaded, and it is loaded heavily, 7r-mode
symmetry may be partially destroyed.
By narrowing the width of the coup-
ling iris, the requisite symmetry can be restored.
no enhancement in the intensity of w-mode radiation.
Nonetheless, we find
(The iris can be
narrowed down up to a point; for gaps that are too narrow, there is evidence of rf breakdown...)
In another experiment the emission from the A6 (and D6) magnetron is
coupled out symmetrically by allowing the radiation to escape in equal
amounts from each resonant cavity.
The emitted radiation is then allowed
to fill a section of cylindrical waveguide 17cm in diameter surrounding
the anode block (see Fig. 9b).
The radiation ultimately leaves the sys-
tem axially via a 17cm plexiglass window.
This manner of coupling leads
to excitation of the TE01(H 0 1 ) waveguide mode, and the cylindrical pipe
with its output window thus behaves as a cylindrical TE 01-mode antenna.
Despite the care taken to preserve symmetry, '-mode emission remains
- 20 weak.
In yet a third experiment, "priming" of the 7r-mode is attempted.
The idea behind this technique is to fill the magnetron with intense radiation at the frequency of the sought-after mode, just prior to firing the
main voltage source.
The suitably primed magnetron is then expected to
"lock onto" the required iT-mode, as the voltage on the device erects.
To
this purpose we constructed magnetron J6 (see Table 1 and Fig. 9c) provided with two capacitive coupling irises.
The one iris is for coupling
out the microwave emission in our usual way; the other iris couples in
500kW of microwave power at a frequency of 2.8GHz, for a period of 2psec.
No noticeable n-mode enhancement is observed in the J6 magnetron.
On the basis of the above experiments we conclude that the lack of
success in operating the relativistic magnetron in the n-mode is due to
the narrow interaction gap, as was discussed in section 2.
4. DISCUSSION
The relativistic magnetron has the potential of becoming an efficient, structurally simple and rugged source of intense, pulsed microwave
power in the centimeter wavelength range.
Because of limitations im-
posed by dc and rf breakdown, it is unlikely to be useful at millimeter
wavelengths where the physical distances between electrodes are small.
Although our experimental tubes are energized with short, tens of nanosecond pulses, one can conceive of generators having microsecond pulse
lengths.
The reason is that in the magnetron geometry, the large ex-
ternally applied axial magnetic field inhibits diode closure caused by
motion of anode and cathode plasma.3 ,1 2
Indeed, relativistic smooth-
bore magnetrons have been operated for one or two microseconds.32
From
the experiments discussed in section 3 above, a good flat-topped voltage
- 21 pulse is mandatory for such long-pulse operation.
Figure 7 shows that the magnetron diode is a high impedance tube
with impedances typically in the range from 20-40 ohms.
Hence, for effi-
cient operation, the pulsed voltage source should be matched to the load,
unlike the situation in our experiments which employ a 4 ohm generator.
Unfortunately, at the present time the matching must be made more or less
empirically.
Not enough is known about the magnetron to enable one to
predict the tube impedance.
We hope that the particle simulation code
under development30 will enable us to perform this task.
Although the relativistic magnetron is an interesting experimental
tube, it has a long way to go before becoming a practical device.
In
particular, a serious materials study needs to be undertaken.
Graphite as cathode material has the advantage of having very good
field emission characteristics
lays.
with one of the smallest erection de-
But, the entire diode becomes easily coated with carbon.
As a re-
sult, tube performance deteriorates rapidly and the diode must be carefully cleaned after each 15-20 successive shots.
like aluminum, steel, or brass should be tried.
Other cathode material,
If long pulse operation
is contemplated, quick erection is not an issue, and molybdenum may prove
satisfactory.
Anode blocks made from aluminum, copper, or tellurium copper suffer
fairly severe damage.
The damage occurs primarily at the resonator "teeth"
and directly opposite to the free end of the emitting cathode (we recall
from section 3 that electron emission is confined to the free end,-and
extends over 1-2cm of length only).
The damage is particularly bad when
the capacitor bank energizing the solenoid fails to fire and whenever
Bz<B*, so that the full current reaches the anode.
replace the anode block after several hundred shots.
Anyway, it is well to
There is no appar-
- 22 ent reason why stainless steel anode blocks could not be used, and we
are presently constructing one such block.
As discussed in section 2, a
low Q seems to be desirable, and steel with its low electrical conductivity may not be harmful.
As one proceeds to higher and higher tube voltages
5,9
and conse-
quently to even higher tube currents, the azimuthal
magnetic field Be
generated by axial current flow 2,13 in the cathode shank, will acquire
more and more importance.
Suppose a current of 30kA flows; it generates
an azimuthal magnetic of 4.0kG at the surface of a 1.5cm radius cathode.
This field is comparable in magnitude to the externally applied axial
field Bz, and may thus have a strong and undesirable influence on the
space charge flow in the interaction gap (the Be field crossed with the
Er field results in an axial drift of the space-charge cloud).
At very
large currents it may well be necessary to suppress the axial current by
feeding the cathode symmetrically from opposite directions.
Alternately,
one can make the cathode in the form of a helical conducting ribbon as is
illustrated in Fig. 14.
If the pitch angle is small enough, B
interaction space can be reduced considerably.
in the
We have constructed and
tested such a ribbon cathode at a current level of ~8kA, and found to
our satisfaction no adverse effect in the rf performance of the tube.
- 23 REFERENCES
1.
G. B. Collins, editor, "Microwave Magnetrons" (McGraw-Hill, 1948).
2. E. Okress, editor, "Crossed-Field Microwave Devices" (Academic
Press 1961) Volumes 1 and 2.
3. G. Bekefi and T. J. Orzechowski, Phys. Rev. Letters 37, 379, (1976).
4. G. Bekefi and T. J. Orzechowski, Am. Phys. Soc. Bull. 21, 571 (1976),
paper DM-4
5. T. J. Orzechowski, G. Bekefi, A. Palevsky, W. M. Black, S. P.
Schlesinger, V. L. Granatstein, and R. K. Parker, Am. Phys. Soc. Bull.
21, 1112 (1976) papers 5G-3, 5G-4.
6. A. Palevsky, R. J. Hansman, Jr., and G. Bekefi, Am. Phys. Soc. Bull.
22, 648 (1977), paper KH-1
7. A. Palevsky and G. Bekefi, Am. Phys. Soc. Bull. 23, 588 (1978) paper
GO-2
8. N. F. Kovalev, B. D. Kol'chugin, V. E. Nechaev, M. M. Ofitserov,
E. I. Soluyanov and M. I. Fuks, Sov. Tech. Phys. Lett. 3(10), 430
(1977) [Pis'ma Zh. Tekh. Fiz.3, 1048 (1977)1; also V. E. Nechaev,
M.I. Petelin and M. I. Fuks, Sov. Tech. Phys. Lett. 3(8), 310 (1977)
(Pis'ma Zh. Tekh. Fiz. 3, 763 (1977)].
9.
A. N. Didenko, A.S. Sulakshin, G. P. Fomenko, Yu. G. Shtein and Yu.
G. Yushkov, Pis'ma Zh. Tekh. Fiz. 4, 10 (1978).
10.
T. H. Martin, IEEE Trans. Nucl. Sci. NS-20, 289 (1973); K. R.
Prestwich, IEEE Trans. Nucl. Sci. NS-22, 975 (1975).
11.
R. L. Jepsen, Ref. 2, Vol. 1, page 359.
12.
T. J. Orzechowski and G. Bekefi, Phys. Fluids 19, 43 (1976).
Also,
G. Bekefi, T. J. Orzechowski, and K. D. Bergeron, "Proceedings of
the First Inernational Topical Conference on Electron Beam Research
and Technology" Albuquerque, 1975, National Technical Information
- 24 Service, U. S. Dept. of Commerce UC-21, Vol. I, page 303 (1976).
13.
T. J. Orzechowski and G. Bekefi, companion paper, called Paper I in
text (to be published)..
14.
R. K. Parker, R. E. Anderson, and C. V. Duncan, J. Appl. Phys. 45,
2463 (1974).
15.
0. Buneman, article in "Crossed-Field Microwave Devices" (Academic
Press 1961) E. Okress editor, Vol. 1, p. 209.
16.
R. V. Lovelace (private communication 1977).
An equation for the
planar magnetron, corresponding to Eq. 3 is given by E. Ott and
R. V. Lovelace, Appl. Phys. Lett. 27, 378 (1975).
17.
N. Kroll, Ref. 1, chapter 2, p. 49; also N. Kroll and W. Lamb,
J. Appl. Phys. 19, 183 (1948).
18.
J. C. Slater, Radiation Laboratory Report No. 43-9, August 31, 1942
Massachusetts Institute of Technology (unpublished).
19.
L. R. Walker, Ref. 1, chapter 4, p. 118.
20.
N. Kroll, Ref. 1, chapter 3, p. 83; also N. Kroll and W. Lamb,
J. Appl. Phys. 19, 183 (1948).
21.
J. Feinstein and R. J. Collier, Ref. 2, Vol.2, chapter 3, p. 123;
also A. J. Bamford, W. A. Gerard, and C. H. Scullin, IEEE Trans.
Electron Devices, ED-14, 844 (1967).
22.
R. K. Parker is building a coaxial magnetron (private communication
1978).
23.
H.A.H. Boot, H. Foster, and S. A. Self, Proc. Inst. Electr. Eng. 105
Part B Suppl. No. 10, p. 419 (1958).
24.
0. Buneman, Ref. 2, Vol. 1, p. 209;
S. P. Yu, G. P. Kooyers, and
0. Buneman, J. Appl. Phys. 36, 2550 (1965).
25.
P. L. Kapitsa, "High Power Microwave Electronics" (Pergamon Press,
New York 1964).
Also, J. F. Hull, Ref. 2, Vol. 1, p. 496.
- 25 26.
M. Karakawa, M.S. Thesis, Department of Physics, M.I.T. 1978
(unpublished).
27.
N. Kroll, Ref. 1, p. 69.
28.
A. J. Hatch, Nuclear Instruments and Methods 41, 261 (1966).
29.
P. F. Clancy, Microwave Journal p. 77, March 1978; B. Bischof,
Nuclear Instruments and Methods 97, 81, (1971).
30. A. Palevsky, A. T. Drobot, and G. Bekefi (to be published).
31.
P. Efthimion, P. R. Smith, and S. P. Schlesinger, Rev. Sci. Instr-.
47, 1059 (1976).
32.
S. C. Luckhardt and H. H. Fleischmann, Appl. Phys. Lett. 30, 182
(1977).
- 26 -
CU
0
'44
o N
'4.
0
0
0
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U
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44
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n
o
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04
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00
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00
rl
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Co
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.
- 27 -
Table 2.
Comparison between computed and measured resonant frequencies
(given in GHz) for the A6 and D6 magnetrons; "cal." means calculated
values; "cold" refers to cold tests as per text; "hot" refers to measurements made when magnetron oscillates at full power.
10, 2 , ...
E
MAGNETRON\
A6
is that used in Ref. 1.
10
2
(n=1,5, .. )(n-2,4,
3
.. )(n-3)
0
0
(n-6)
cal.
1.35
2.12
2.34
4.60
cold
1.54
2.17
2.41
4.55
2.3
4.6
hot
D6
The mode nomenclature
cal.
1.13
1.81
1.98
4.01
cold
1.20
1.82
2.00
3.90
hot
3.9
(n=1,5,..)
4.97
4.20
- 28 FIGURE CAPTIONS
Fig.
1.
Schematic of a magnetron.
cathode.
The inner cylinder is the emitting
The outer cylinder is the anode.
axial magnetic field B
I
z
There is a uniform
pointing into the page.
d-ra-r , called the interaction space, iL
The region
partially filled
with electron space-charge rotating in the clockwise direction.
Fig.
2. The region of operation of the A6 magnetron is delineated by
the two solid curves derived from Eqs. 1 and 3. The dashed
line is from experiment.
At the position of the solid dot the
magnetron emits at maximum power.
Fig.
3.
RF admittances Y computed for the A6 magnetron, as a function
of frequency w.
The solid lines are the admittances of the
(empty) interaction space spatially averaged over the opening
to the resonators (at r-r a and $/2<e<*/2).
The dashed line is
the admittance of the vane-type resonators, averaged over the
opening to the interaction space.
The points of intersection
give the oscillation frequencies.
The mode nomenclature fol-
lows that adopted in Ref. 1, chapter 2.
Fig.
4.
Dispersion diagram for the modes of the A6 magnetron.
The slope
of a straight line drawn from the origin (as for example the
dashed line) gives the phase velocity of a given mode in units
of segments per second.
Fig.
5. The rf electric fields of the 7r(n-3) and 27r(n-6) modes of the
A6 magnetron.
The circular dashed line gives the outer radial
boundary of the Brillouin space charge (prior to the onset of
rf fluctuations).
-29Fig.
6. The same as Fig. 5 calculated for the HP10V tube.
Note the
large width dra-rc of the interaction space of this tube
compared with that of the A6 tube of Fig. 5.
Fig.
7. The voltage-current charcteristics of the A6 magnetron as a
function of magnetic field.
The current is the total radial,
plus any residual, axial current.
Fig.
8. Measured total and axial currents in the D6 magnetron as a
function of magnetic field.
The latter is due mainly to
tube misalignment and asymmetries.
Fig.
9. RF coupling circuits.
Fig. 10.
Voltage, current and microwave pulse shapes.
Note the small
width of the microwave signal compared with that of the voltage
pulse.
Fig. 11.
Microwave power emitted from the A6 magnetron as a function of
magnetic field.
Fig. 12.
At B =7.6kG, the peak power is ~0.90GW.
The effect of metal end-caps on the emission characteristics
of the D6 magnetron.
The solid line is for the case with end-
caps, the dashed line is for no end-caps.
At B =4.9kG, the
z
peak power (with end-caps) is -0.4GW.
Fig. 13.
Spectral characteristics of the power emitted from the A6 magnetron, (a) under single mode operation, (b) in the presence of
mode breakup, and (c) in the presence of multimoding.
In each
case the trace to the far left is the reference, undispersed,
signal.
On the right are the dispersed signals.
- 30 Fig. 14.
Sketch of a carbon cathode machined in the form of a helical
ribbon to reduce B
in the interaction space.
Fig. 1
r4
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Fig. 4
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Fig. 9
I 251 kV
DIODE.
VOLTAGE
20 ns
(a)
8.7 kA
DIODE
CURRENT
20 ns
(b)
CRYSTAL
VOLTAGE
--
I 20 mV
20 ns
(c)
Fig. 10
I
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00 ns
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a-
z
(D)
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0
(b)
100 ns
(c)
I
TIME (psec) 0
I
I
I I
0.2
I
0.4
I
I
0.6
1
FREQUENCY (GHz)
I
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